Sunday, February 27, 2005

Two fellow (and slightly better known) Chicago professors Gary Becker
and Richard Posner run a joint weblog on various social
issues. This week they tackle the question of whether the faculty "own"
a university. Becker says
yes and Posner says
no. I have to go with no. I believe the board of trustees acts as
the owners on behalf of the "shareholders" known as
alumni. Many professor do act for the betterment of the university but
professors come and go are no more owners than players on a baseball
team.

Another question that comes up in discussions is who are the
university's customers? Some possible answers:

Students. But why is their success based on their performance?

The Government who give the grants for research.

The employers of the students.

Society at large.

Perhaps the mistake is in making the analogy between university and
corporation.

Friday, February 25, 2005

I'm off to Japan for a Workshop on New Horizons
in Computing that kicks off a new theory
project sponsored by the Japanese Ministry of Education. This will
be my first time in Kyoto and my first trip to Japan since I was
stranded there after September 11. Let's hope history doesn't repeat
itself.

I'll be talking about my favorite theorems of the past decade but you,
my loyal weblog readers, have seen it here first.

Tuesday, February 22, 2005

We know only a few natural problems in NP that are not known to be
NP-complete or in P. The two most often named are factoring and graph
isomorphism. Another that has come to forefront is Nash Equilibrium.

Given two n x m matrices A and B, consider the game where
simultaneously player I picks a row i and player II picks a column
j. Player I's payoff is A(i,j) and player II's payoff is B(i,j).

Nash proved that for all A and B there are probability distributions
σ on the rows and τ on the columns so that if the player I
plays according to σ and player II plays according to τ

There is no i such that if player I chooses row i his expected
payoff will increase with player II still playing according to τ.

There is no j such that if player II chooses column j her expected
payoff will increase with player I still playing according to σ.

The computational problem is to find σ and τ given A and
B. It's a major open question whether a polynomial-time algorithm exists.

Using linear programming we can find Nash Equilibrium in a zero-sum
game (A(i,j)=-B(i,j) for all i,j) or if we know the set of i where
σ(i)=0 and the j where τ(j)=0.

We can also find a correlated equilibrium in polynomial-time which is
a distribution on pairs (i,j). However to implement a correlated equilibrium
you need either a third trusted party or use some cryptographic
techniques.

I don't know a good survey on the complexity of Nash Equilibrium but perhaps my readers will have some good references.

Saturday, February 19, 2005

Last night's NUMB3RS again centered around complexity. A brilliant
mathematician (not Charlie) tells his friends that he's on the verge of
proving the Riemann hypothesis -- and not only that, but his proof will
somehow yield a fast factoring algorithm. When the bad guys get wind of
this, they kidnap the mathematician's six-year-old daughter, demanding
the algorithm as ransom. But the mathematician refuses to cooperate
with the FBI investigation of the kidnapping. The reason, we later
learn, is that the mathematician has fooled himself: he doesn't
have a proof or an algorithm, and he's terrified the bad guys will find
out. (One thing that has to be said for NUMB3RS: in contrast to, say,
Good Will Hunting, it does get across the idea that math problems
are hard.) So Charlie has the improbable task of helping the
other mathematician fake a factoring algorithm -- apparently, the
bad guys won't be savvy enough to run whatever they get on a few random
instances!

In a way, this episode represents a retreat from the premise that
"math helps us solve crimes" -- I mean, no duh it helps, if the
crimes in question happen to involve polynomial-time factoring
algorithms! But in my opinion, the fact that math was actually integral
to the plot helped to make this the most effective episode so far. In
contrast to the P versus NP episode, this time they actually explained a
little about prime numbers, RSA, and factoring, and did a fairly
non-egregious job by TV standards. Admittedly, an RH proof leading to a
factoring algorithm seems pretty farfetched, but what path to efficient
factoring isn't farfetched? (Other than building a quantum
computer, of course.)

My main criticism is that, whenever Charlie and the other academics
open their mouths, I feel like I'm listening to foreigners speaking
perfectly grammatical sentences that no native speaker would ever utter.
The phrasing is just too pretentious -- a trivial example being that
everyone calls the Riemann hypothesis "Riemann's hypothesis." If they
wanted to, the writers could easily fix this problem by reading the
scripts to mathematicians, and seeing which lines pass the cringe test.

Friday, February 18, 2005

I've already heard from several graduating students who have had few
or no interviews scheduled and are really worried about finding a job
next year. Don't panic yet.

CS recruiting is not a well coordinated affair running from January to
June and often beyond. Each department determines their needs and
resources and invites candidates for interviews, makes some of them
offers and makes later interviews and offers as the first offers are
turned down or as resources change, like a current faculty
member decides to go somewhere else.

What does this mean? There is a small set of top candidates that get
most of the interviews and initial offers. Some of these candidates can
tie up offers for months because they are waiting for some other
university to decide or they are simply indecisive and no one puts
pressure on them to decide.

For students not in this top group they will get few or no early
interviews and feel like they will never get a job. The market will
shake itself out and dig deeper into the applicant pool. Departments
that have theory as a secondary priority will realize they can't find
good candidates in their top priority and start looking at theory
candidates. In short the recruiting is game is just beginning.

Meanwhile broaden your search and look at places you may not have
considered before. Work on your job talk even before you have anything
scheduled and give a practice talk in your department.
But mostly keep busy and get your mind off the job
market. I found working hard on the thesis helps.

Wednesday, February 16, 2005

I've seen several pointers to this nice article
on origami and Erik Demaine in the Science Times section of yesterday's New
York Times but also check out today's editorial
page.

Thanks to pressure from prestigious academic and scientific
organizations and leaders of high-tech industries, the administration
added staff and streamlined the [student visa] process so clearance
now takes less than two weeks, on average.

The capstone was a policy change announced last week that made a
clearance valid for four years for students and two years for working
scientists, making it easier for them to stay in the country for the
duration of their study or research. America's reputation for
welcoming scholars from around the world can only benefit.

We should always treat such news cautiously but hopefully these new
policies will encourage more foreign students to come study in the states.

Update: Also in today's Times, an article announcing the ACM Turing Award that went to Robert Kahn and Vinton Cerf for their early work on the internet. The Turing Award is the closest computer science has to the Nobel Prize and its nice to see the New York Times taking it as such.

Monday, February 14, 2005

How should you decide whether to go into industry? Are there ways back
after you have sold your soul?
The occasion: I got an offer from a major internet company to work at
one of their labs. I
have until Monday to decide. At this moment, I don't have any promising
leads to do the research I'm interested in inside academia. My advisor
says that if I
don't like it at this company I can always come back, but I am a bit doubtful
of that…what is your take on this?

It depends on the kind of industrial lab and how long before you would
go back into academics. If you go to a basic research lab and continue
to produce academic papers then you can find an academic job
afterwords. You'll lose a little by not having teaching experience but
that gets offset by having more time for research.

If on the other hand you go to an industrial job for even a couple of
years and don't continue to produce academic research papers or attend
conferences it will be very difficult to find an academic job
afterwords particularly in a theoretically oriented field.

If you really want to stay in academics take an academic job that
might not be to your liking and work hard to produce good research and
try again later.

Do any of you readers have stories of people that have successfully
gone from industrial jobs back to academics?

Saturday, February 12, 2005

I have one word of advice that applies especially to junior faculty: No.

You will be asked to referee papers, look at graduate applications,
look a faculty applications, write reports and recommendation
letters. You will be asked to sit on committees: curriculum
committees, space committees, program committee, web page committees,
budget committees, planning committees and other committees you would
never have imagined. You'll have committee meetings at the
departmental, divisional and university levels as well as committees
to serve the broader theory community. You will be asked to organize
workshops, conferences and edit special issues. You'll also be
teaching, writing grants and going to faculty meetings.

All of the above are good things to do. But do all of the above and
you'll never get tenure. You need time for research. So learn to limit
yourself, learn to say "no". I'm not saying not to do any of
the above. Most of these tasks have to get done; you should do your
fair share and be a "good citizen". But you don't need to
agree to every request, feel free to turn down requests when you feel
yourself getting overloaded. If you gain a reputation as someone who
can't say "no" people will take advantage of you. And don't
fall for the "You are the only one who can do a good job"
ploy.

If you try to do too much you won't do anything particularly well. I
would much rather have someone say "no" to me than saying
"yes" and doing a mediocre job.

This paper formalizes the idea that we now all take as obvious
that we should use Turing machines to determine complexity of
complexity by measuring time as a function of the
size of the input. Ever since the Hartmanis-Stearns paper we measure
nearly every resource (time, space, random bits, circuit depth, etc.)
as a function of the input size.

This paper also gives the first hierarchy of classes, showing that for
nice functions t and u with t2(n)=o(u(n)) then there are
problems solvable in time u(n) but not time t(n) on multitape Turing
machines. Soon later Hennie and Stearns showed the same
result if t(n) log t(n) = o(u(n)).

While initially the smart money was on P ≠ NP, today increasingly
the belief is that the statement P=NP is independent of the other
axioms of mathematics. Few believe P=NP.

For the record NP stands for "Nondeterministic
Polynomial-Time" (not a joke) and at least this complexity
theorist feels that a proof of P≠NP exists and we just haven't
found it yet. Just because we are too stupid to find the proof doesn't
mean the problem is independent.

I don't mean to be hard on Garrity. He should be lauded for
including the P versus NP problem in his book.

Tuesday, February 08, 2005

Suresh has been doing a fine jobreviewing
the Numb3rs episodes. Nevertheless Bill Gasarch wanted to write a
guest post on the P versus NP episode which was the second episode
broadcast and not the fourth as I had previously mentioned. But first
my comment to Charlie: Don't let your brother mess up your
priorities. Go back to solving P versus NP. So what if a few bank
robbers get away?

Now on to Bill's Guest Post:

REVIEW OF SECOND EPISODE OF NUMB3RS
USE OF P vs NP.

This is the `P vs NP' episode.

"Are you still working on that P vs P thing"

"Its the P vs NP thing"

They mentioned P vs NP ALOT of times.

PROS: ANY mention of our favorite problem on TV is good.
This may be the first mention of P vs NP on an
entertainment show since Homer Simpson fell into
the third dimension where there were all kinds of equations
floating around in the background including P = NP.

CONS: Wasted Opportunity. They made NO attempt to explain
the problem. Could they have? Trying to color a map with 3 colors
might be the problem easiest to explain. Or TSP.
Might be hard to tie that to a crime, but
minesweeper is also contrived.
For that matter, could they have explained minesweeper better,
and add something like
"One way to solve it is to look at all possibilities.
Even with really powerful computers, that could take to long.
We want to know, is there a faster way?"
I would not even try to explain NP or `checkability'
I would just say that here are problems we can solve by
looking at all possibilities, and we want to know if
we can do substantially better.

ODD POINT: They mentioned a few times that it was `unsolvable'
What did they mean?
Options-

Charlie was trying to prove P=NP and this is unlikely to be true

Charlie was using techniques from recursion theory that likely
to not work because of the oracles. (the what?)

Charlie was using proofs that naturalize, which won't work because
of the results of Razborov and Rudich (Judd Hirsch: So use unnatural techniques)

The problem is independent of PA

The problem is independent of ZFC

The problem is just very very hard.

Likely they meant 1 or 6 (SARCASM ALERT: 2-5 were not meant to be taken
seriously).
But they should have spoken more clearly about this.

PRO: They do (in general, not just this episode) show Math in a good light
and show Mathematicians in a good light.

PREDICTION: Will be canceled within 1.5 years. Don't need
Charlie's math to predict that.

Monday, February 07, 2005

My old apartment-mate Eric Schwabe came over to watch the game last
night and brought along old posters he had from the Super Bowl parties
we used to throw as grad students at MIT. The Lance Fortnow
Super Bowl Party continued at MIT after I left with a much larger
crowd in my absence. A few years later it morphed into the Who the
Hell is Lance Fortnow Super Bowl Party. Around this time (about
1992) an MIT student was excited to meet me at STOC not because of any
research I had done but because he had been to "my" party.
Eventually even the memory of the memory of me faded away and so did
the party.

What happens now? We invited a few friends over for the game, every
single one of which left early to put their respective kids to bed.

Saturday, February 05, 2005

The DIMACS Workshop on Information Markets drew a neat crowd, a mix of
computer scientists, economists (mostly experimental) and members of
industry from companies as big as Microsoft and so small they are run
by individuals in their spare time. Information markets create securities
that can aggregate people's beliefs and help predict the likelihood of
future events.

This workshop reminded me of the early conferences in quantum
computing a decade ago. Quantum computing back then had some promising
research (factoring algorithms for example) and no one was sure
whether it would lead to whole new computing paradigm or just
disappear into the ether. Information markets are also
a new technology with some promising research (mostly analytic and
experimental) and no one knows whether it will revolutionize the way
everyone does prediction, information aggregation and decision making or
just slowly disappear.

Information markets face different challenges than quantum
computing. The technology already exists to run efficient markets and
better tools are being developed. However the field needs to convince
business and governmental leaders of the value and accuracy of the
markets, overcome the stigma from the terrorism
futures scare
and find ways to overcome the legal issues relating
to gambling in running real money markets.

Quantum computing needs to deal merely with the laws of physics but
information markets need to deal with the laws of the United States
of America.

Thursday, February 03, 2005

One of my students wanted me to complain in my weblog at the lack of
wireless access in conferences like the recent SODA meeting. Sorry but I
don't agree. I've discussed before how I find internet at conferences
reduces
conversation between participants and prevents us from
escaping from work back home. Is it so bad that the SODA participants
were forced to (gasp) talk to each other?

On that note let me finish this post so I can pay attention to the talk.

Wednesday, February 02, 2005

Each day a weatherman gives a probability p of rain for the next day and
each day it either rains or it doesn't. How do we judge the quality of
these forecasts? A first attempt uses linear scores, p if it rains,
1-p if it doesn't. However when you analyze this system the weatherman
should predict p=1 if his belief is greater than 1/2 and p=0
otherwise.

A better measure is the log loss. The weatherman gets penalized -log(p)
if it rains and -log(1-p) if it doesn't. A weatherman now has the
incentive to announce his belief. There are other scoring functions
with this property but the log loss has some nice properties such as
the best a weather could hope to achieve is exactly the entropy of the
distribution. The log loss and other measures are often used to
analyze prediction mechanisms such as information markets.

Dean Foster and Rakesh Vohra have a different take looking at a notion
called
calibration. Here you take all the days that the weatherman predicted
70% chance of rain and check that 70% of those days it actually
rained. A prediction algorithm calibrates a binary sequence if for
finite set of allowed probabilities, each of the subsequences consisting
of predictions of probability p have about a p fraction of
ones. Foster and Vohra showed
that some probabilistic calibration scheme will calibrate every
sequence in the limit. In other words you can be a great weatherman in
the calibration sense just by looking at the history of rain and
forgoing that pesky meterological training.

Dean Foster and Sham
Kakade gave a couple of interesting talks at the Bounded Rationality
workshop giving a deterministic scheme that achieves a weak form of
calibration and use it to learn Nash equilibirum in infinite
repeated games.